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start_sparse_kit.f90
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start_sparse_kit.f90
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MODULE start_sparse_kit
USE sparse_matrix_profiles
USE global_variables ! MPI variables
IMPLICIT NONE
SAVE
PRIVATE :: sort_pick
CONTAINS
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
SUBROUTINE start_matrix_2d_p1 (np, jj, js, AA)
!+++++++++++++++++++++++++++++++++++++++++++++++
! Construction of the CSR data structure for matrix AA
! Matrix AA can be nonsymmetric. The column indices of
! the nonzero matrix elements are ordered increasingly
! LINEAR TRIANGULAR ELEMENTS
! The diagonal element in each row is assumed to be different from zero
! np ---> number of nodes of the grid == order of matrix AA
!
! jj ---> standard element-to-node topology of the fem grid
!
! js ---> array of the node numbers of all boundary nodes (global numbering)
!
! AA ---> matrix in CSR format (DERIVED TYPE)
IMPLICIT NONE
INTEGER, INTENT(IN) :: np
INTEGER, DIMENSION(:,:), INTENT(IN) :: jj
INTEGER, DIMENSION(:), INTENT(IN) :: js
TYPE(CSR_MUMPS_Matrix), INTENT(OUT) :: AA
INTEGER, DIMENSION(np) :: nz_el_in_each_row
INTEGER :: i, j, m, NA_nz, v, w, k, l
ALLOCATE (AA % i(np+1))
nz_el_in_each_row = 1
DO m = 1, SIZE(jj,2)
nz_el_in_each_row(jj(:,m)) = nz_el_in_each_row(jj(:,m)) + 1
ENDDO
! correction for the boundary nodes
nz_el_in_each_row(js) = nz_el_in_each_row(js) + 1
! definition of the first (nz) element of each row
AA % i(1) = 1
DO i = 1, np
AA % i(i+1) = AA % i(i) + nz_el_in_each_row(i)
ENDDO
NA_nz = AA % i(np+1) - 1
ALLOCATE (AA % j(NA_nz), AA % e(NA_nz))
! column indices of all nonzero elements
AA % j = 0
DO m = 1, SIZE(jj,2)
DO v = 1, SIZE(jj,1); i = jj(v,m)
k = AA % i(i) ! first element of the row
l = AA % i(i+1) - 1 ! last element of the row
DO w = 1, SIZE(jj,1); j = jj(w,m)
IF (ANY(AA % j(k:l) == j)) CYCLE
! forward shift and stack of the new element
AA % j(l : k+1 : -1) = AA % j(l-1 : k : -1)
AA % j(k) = j
ENDDO
ENDDO
ENDDO
! sort in scending order of the column indices of each row
DO i = 1, np
k = AA % i(i) ! first element of the row
l = AA % i(i+1) - 1 ! last element of the row
CALL sort_pick ( AA % j(k : l) )
ENDDO
!======================================================================
!!!!!!!!!!!! MODIFIED !!!!!!!!!!!!!!!!!
ALLOCATE ( AA % i_mumps (SIZE(AA%j)) )
DO i = 1, SIZE(AA%i)-1
DO j = AA%i(i), AA%i(i+1)-1
AA%i_mumps(j) = i
ENDDO
ENDDO
!======================================================================
WRITE (*,*) ' CSR matrix structure for the P1 grid completed'
END SUBROUTINE start_matrix_2d_p1
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
SUBROUTINE start_matrix_2d_p2 (np, jj, js, AA)
!+++++++++++++++++++++++++++++++++++++++++++++++
! Construction of the CSR data structure for matrix AA
! Matrix AA can be nonsymmetric. The column indices of
! the nonzero matrix elements are ordered increasingly
! PARABOLIC TRIANGULAR ELEMENTS
! The diagonal element in each row is assumed to be different from zero
! np ---> number of nodes of the grid == order of matrix AA
!
! jj ---> standard element-to-node topology of the fem grid
!
! js ---> array of the node numbers of all boundary nodes (global numbering)
!
! AA ---> matrix in CSR format (DERIVED TYPE)
IMPLICIT NONE
INTEGER, INTENT(IN) :: np
INTEGER, DIMENSION(:,:), INTENT(IN) :: jj
INTEGER, DIMENSION(:), INTENT(IN) :: js
TYPE(CSR_MUMPS_Matrix), INTENT(OUT) :: AA
INTEGER, DIMENSION(np) :: nz_el_in_each_row
INTEGER :: i, j, m, NA_nz, v, w, k, l, ii, c
ALLOCATE (AA % i(np+1))
! preliminary determination of the boundary nodes that
! are mid-side nodes to have the right correction for
! all boundary nodes, including the mid-side ones.
nz_el_in_each_row = 0
DO m = 1, SIZE(jj,2)
nz_el_in_each_row(jj(:,m)) = nz_el_in_each_row(jj(:,m)) + 1
ENDDO
WHERE (nz_el_in_each_row == 1)
nz_el_in_each_row = - 1
ELSEWHERE
nz_el_in_each_row = 0
END WHERE
! end of the preliminary countercorrection phase
nz_el_in_each_row = nz_el_in_each_row + 1
DO m = 1, SIZE(jj,2)
nz_el_in_each_row(jj(1:3,m)) = nz_el_in_each_row(jj(1:3,m)) + 3
nz_el_in_each_row(jj(4:6,m)) = nz_el_in_each_row(jj(4:6,m)) + 4
ENDDO
! correction for all boundary nodes
nz_el_in_each_row(js) = nz_el_in_each_row(js) + 2
! definition of the first (nz) element of each row
AA % i(1) = 1
DO i = 1, np
AA % i(i+1) = AA % i(i) + nz_el_in_each_row(i)
ENDDO
NA_nz = AA % i(np+1) - 1
ALLOCATE (AA % j(NA_nz), AA % e(NA_nz))
!+++ Edited by Pier
ALLOCATE ( AA % i_mumps (NA_nz) )
c = 1
DO i = 1, np
DO ii = AA%i(i), AA%i(i+1) -1
AA%i_mumps(c) = i
c = c + 1
END DO
END DO
!+++
! column indices of all nonzero elements
AA % j = 0
DO m = 1, SIZE(jj,2)
DO v = 1, SIZE(jj,1); i = jj(v,m)
k = AA % i(i) ! first element of the row
l = AA % i(i+1) - 1 ! last element of the row
DO w = 1, SIZE(jj,1); j = jj(w,m)
IF (ANY(AA % j(k:l) == j)) CYCLE
! forward shift and stack of the new element
AA % j(l : k+1 : -1) = AA % j(l-1 : k : -1)
AA % j(k) = j
ENDDO
ENDDO
ENDDO
! sort in scending order of the column indices of each row
DO i = 1, np
k = AA % i(i) ! first element of the row
l = AA % i(i+1) - 1 ! last element of the row
CALL sort_pick ( AA % j(k : l) )
ENDDO
WRITE (*,*) ' CSR matrix structure for the P2 grid completed'
END SUBROUTINE start_matrix_2d_p2
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
SUBROUTINE start_coupled_system_axisym (np, np_L, jj, js, CC)
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
! Cylindrical coordinate for Axisymmetric problems with swirl
! generation of the CSR structure of the matrix CC
! of the coupled velocity-pressure system with
! interpolations of different order (p2-p1) from that
! of the matrix AA of the uncoupled system with the
! parabolic interpolation (p2) of the velocity component.
! The CSR structure of the coupling rectangular part
! is based on the assumption that all the linear nodes
! of the grid precede all the remaining midside-nodes
! of the parabolic interpolation
IMPLICIT NONE
! input variables
INTEGER, INTENT(IN) :: np, np_L
INTEGER, DIMENSION(:,:), INTENT(IN) :: jj
INTEGER, DIMENSION(:), INTENT(IN) :: js
! output variables
TYPE(CSR_MUMPS_Matrix) :: CC
! local variables
TYPE(CSR_MUMPS_Matrix) :: AA
INTEGER, DIMENSION(np) :: nz_RR
INTEGER, DIMENSION(np + 1) :: RR_i
INTEGER, DIMENSION(np_L) :: nz_RT
INTEGER, DIMENSION(np_L + 1) :: RT_i
INTEGER, DIMENSION(:), ALLOCATABLE :: RR_j, RT_j
! INTEGER, DIMENSION(:,:), ALLOCATABLE :: RR
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
! 2 modifiche fatte da Auteri
! INTEGER, DIMENSION(np) :: column
INTEGER, DIMENSION(np_L) :: col_num
! e` anche stato eliminato l'IF (SAVE_MEMORY)
! perche' porlo uguale a .FALSE. comporta un uso
! di memoria eccessivo.
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
INTEGER :: NR, size_CC, k, i, j, iA, ii, p, n, c
! executable statements
WRITE(*,*)
WRITE(*,*) '+++++++++++++++++++++++++++++++++++++'
WRITE(*,*) '--> Creating Jacobian matrix sparse structure'
!+++
CALL start_matrix_2d_p2 (np, jj, js, AA)
!+++
! preliminar counting of the coupling rectangular part
DO i = 1, np
k = 0
DO p = AA%i(i), AA%i(i+1) - 1
IF (AA%j(p) <= np_L) k = k + 1
ENDDO
nz_RR(i) = k
ENDDO
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
! modifica 1 di Auteri:
nz_RT = 0
DO n = 1, SIZE(AA%j)
j = AA%j(n)
IF (j <= np_L) nz_RT(j) = nz_RT(j) + 1
END DO
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
! Consistency check
NR = SUM(nz_RR)
ALLOCATE (RR_j(NR), RT_j(NR))
WRITE (*,*) '--> Consistency check'
WRITE (*,*) ' SUM(nz_RR) = ', SUM(nz_RR)
WRITE (*,*) ' SUM(nz_RT) = ', SUM(nz_RT)
WRITE (*,*) ' tot from the first np_L rows of AA = ', AA%i(np_L+1) - 1
WRITE (*,*)
IF (NR /= AA%i(np_L+1) - 1) THEN
WRITE (*,*) 'incoherence between NR and AA%i(np_L+1) - 1'
WRITE (*,*) 'in start_coupled_system. STOP'
CALL MPI_ABORT(MPI_COMM_WORLD, mpiErrC, mpiIerr)
ENDIF
! ALLOCATION OF THE STRUCTURE FOR CC OF THE COUPLED SYSTEM
size_CC = 9 * SIZE(AA%j) + 6 * NR
! bottom-right last diagonal element
size_CC = size_CC + 1
WRITE (*,*) ' size_AA = ', SIZE(AA%j)
WRITE (*,*) ' size_CC = ', size_CC
ALLOCATE( CC%i(3*np + np_L + 1) )
ALLOCATE( CC%i_mumps(size_CC), CC%j(size_CC), CC%e(size_CC) )
! DEFINE THE COLUMN INDICES OF THE RECTANGULAR ARRAY RR
! first, the pointer vector RR_i
RR_i(1) = 1
DO i = 1, np
RR_i(i+1) = RR_i(i) + nz_RR(i)
ENDDO
! then, the column indices of RR
k = 0
DO i = 1, np
DO p = AA%i(i), AA%i(i+1) - 1
IF (AA%j(p) <= np_L) THEN
k = k + 1
RR_j(k) = AA%j(p)
ENDIF
ENDDO
ENDDO
! 1 <= RR_j <= np_L
! CONSTRUCTION OF THE TRANSPOSED RECTANGULAR ARRAY RT
! first, the pointer vector RT_i
RT_i(1) = 1
DO i = 1, np_L
RT_i(i+1) = RT_i(i) + nz_RT(i)
ENDDO
! then, the column index vector RT_j ! More difficult
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
! modifica 2 di Auteri:
col_num = 0
DO ii = 1, np
DO p = RR_i(ii), RR_i(ii+1)-1
j = RR_j(p)
col_num(j) = col_num(j) + 1
RT_j(RT_i(j) + col_num(j) - 1) = ii
END DO
END DO
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
! SET THE NUMBER OF nz-ELEMENTS OF THE ROWS
! OF THE MATRIX CC OF THE COUPLED SYSTEM
CC%i(1) = 1
! first block-row
DO i = 1, np
CC%i(i+1) = CC%i(i) + 3 * (AA%i(i+1) - AA%i(i)) + nz_RR(i)
ENDDO
! second block-row
DO i = np + 1, 2*np
iA = i - np
CC%i(i+1) = CC%i(i) + 3 * (AA%i(iA+1) - AA%i(iA)) + nz_RR(iA)
ENDDO
! third block-row
DO i = 2*np + 1, 3*np
iA = i - 2*np
CC%i(i+1) = CC%i(i) + 3 * (AA%i(iA+1) - AA%i(iA)) + nz_RR(iA)
ENDDO
! bottom rectangular block-row: USE TRANSPOSED ARRAY RT
DO i = 3*np + 1, 3*np + np_L
iA = i - 3*np
CC%i(i+1) = CC%i(i) + 3 * nz_RT(iA) ! == (RT_i(iA+1) - RT_i(iA))
ENDDO
! bottom-right last diagonal element
CC%i(3*np + np_L + 1) = CC%i(3*np + np_L + 1) + 1
! DEFINITION OF THE COLUMN INDICES
!=================================
! first block-row
k = 0
DO i = 1, np
DO p = AA%i(i), AA%i(i+1) - 1
k = k + 1
CC%j(k) = AA%j(p)
ENDDO
DO p = AA%i(i), AA%i(i+1) - 1
k = k + 1
CC%j(k) = AA%j(p) + np
ENDDO
DO p = AA%i(i), AA%i(i+1) - 1
k = k + 1
CC%j(k) = AA%j(p) + 2*np
ENDDO
DO p = AA%i(i), AA%i(i+1) - 1
IF (AA%j(p) <= np_L) THEN
k = k + 1
CC%j(k) = AA%j(p) + 3*np
ENDIF
ENDDO
ENDDO
! second block-row
DO i = np + 1, 2*np
iA = i - np
DO p = AA%i(iA), AA%i(iA+1) - 1
k = k + 1
CC%j(k) = AA%j(p)
ENDDO
DO p = AA%i(iA), AA%i(iA+1) - 1
k = k + 1
CC%j(k) = AA%j(p) + np
ENDDO
DO p = AA%i(iA), AA%i(iA+1) - 1
k = k + 1
CC%j(k) = AA%j(p) + 2*np
ENDDO
DO p = AA%i(iA), AA%i(iA+1) - 1
IF (AA%j(p) <= np_L) THEN
k = k + 1
CC%j(k) = AA%j(p) + 3*np
ENDIF
ENDDO
ENDDO
! third block-row
DO i = 2*np + 1, 3*np
iA = i - 2*np
DO p = AA%i(iA), AA%i(iA+1) - 1
k = k + 1
CC%j(k) = AA%j(p)
ENDDO
DO p = AA%i(iA), AA%i(iA+1) - 1
k = k + 1
CC%j(k) = AA%j(p) + np
ENDDO
DO p = AA%i(iA), AA%i(iA+1) - 1
k = k + 1
CC%j(k) = AA%j(p) + 2*np
ENDDO
DO p = AA%i(iA), AA%i(iA+1) - 1
IF (AA%j(p) <= np_L) THEN
k = k + 1
CC%j(k) = AA%j(p) + 3*np
ENDIF
ENDDO
ENDDO
! bottom rectangular block-row
DO i = 3*np + 1, 3*np + np_L
iA = i - 3*np
DO p = RT_i(iA), RT_i(iA+1) - 1
k = k + 1
CC%j(k) = RT_j(p)
ENDDO
DO p = RT_i(iA), RT_i(iA+1) - 1
k = k + 1
CC%j(k) = RT_j(p) + np
ENDDO
DO p = RT_i(iA), RT_i(iA+1) - 1
k = k + 1
CC%j(k) = RT_j(p) + 2*np
ENDDO
ENDDO
! bottom-right last diagonal element
k = k + 1
CC%j(k) = 3*np + np_L
!+++ Edited by Pier
c = 1 ! COUNTER !
DO i = 1, 3*np + np_L
DO ii = CC%i(i), CC%i(i+1) - 1
CC%i_mumps(c) = i
c = c + 1
ENDDO
END DO
!+++
WRITE (*,*) ' CSR start_coupled_system completed.'
END SUBROUTINE start_coupled_system_axisym
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
SUBROUTINE sort_pick (arr)
! sorts an integer array arr into ascending numerical order, by stright
! insertion. arr is replaced on output by its sorted rearrangement.
! Not parallelizable. Very inefficient for SIZE(arr) > 20.
! Adapted from: Numerical Recipes in Fortran 90, p. 1167
IMPLICIT NONE
INTEGER, DIMENSION(:), INTENT(INOUT) :: arr
INTEGER :: aj, i, j
DO j = 2, SIZE(arr); aj = arr(j)
DO i = j - 1, 1, -1
IF (arr(i) <= aj) EXIT
arr(i+1) = arr(i)
ENDDO
arr(i+1) = aj
ENDDO
END SUBROUTINE sort_pick
END MODULE start_sparse_kit